The ratio of the price of a pen to the price of a ruler is 4:3. If the price of a ruler increases by 70p, then the ratio becomes 4:5.
Complete these sentences.
(a) The price of a pen is £
(b) The price of a ruler before the increase is £

(a) The price of the pen is $1.4

(b) The price of the ruler before the increase is $1.05

Step-by-step explanation:

∵ The ratio of the price of a pen to the price of a ruler is 4: 3

→ Multiply each term of the ratio by m, where m is a constant

∴ The cost of the pen = 4m

∴ The cost of the ruler = 3m

∵ The price of a ruler increases by 70p

→ Change 70 p to dollars by divide it by 100

∴ The price of a ruler increases by $0.7

∵ The old price of the ruler = 3m

∴ The new price of the ruler = 3m + 0.7

∵ The ratio between the pen and the ruler becomes 4: 5

∴ The price of the pen/the new price of the ruler =  

∴ The new ratio of the prices =

→ Equate the fraction of the ratio by the fraction of the prices

∴ =

→ By using cross multiplication

∵ 5 × (4m) = 4 × (3m + 0.7)

∴ 20m = 4(3m) + 4(0.7)

∴ 20m = 12m + 2.8

→ Subtract 12 m from both sides

∴ 8m = 2.8

→ Divide both sides by 8 to find m

∴ m = 0.35

(a)

∵ The price of the pen = 4m

∵ m = 0.35

∴ The price of the pen = 4(0.35)

∴ The price of the pen = $1.4

(b)

∵ The price of the ruler before the increase = 3m

∵ m = 0.35

∴ The price of the ruler before the increase = 3(0.35)

∴ The price of the ruler before the increase = $1.05

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

the least value out of the data shown is 5, maybe if you post a picture with it i could a little more.

step-by-step explanation: